In a large pot over medium heat, melt the butter. Add the ham, onion, carrot, and celery. Sprinkle with salt and pepper. Cook until softened, 5-7 minutes.
Add garlic, and cook an additional minute. Add in the split peas.
Stir in the chicken stock, beef stock, and water. Add in the paprika, bay leaf, thyme, and liquid smoke.
Simmer, uncovered, for 60-90 minutes, stirring occasionally, or until the split peas and cooked down and soup is thick.